New London mayor Sadiq Khan has hit out at Donald Trump's "ignorant" view of Islam after the US presidential hopeful suggested he would exempt him from his proposed ban on Muslims entering America.

Mr Trump, who is widely expected to be confirmed as the Republican candidate for the presidency, appeared to extend an olive branch to Mr Khan when he welcomed his election as the first Muslim mayor of a major European capital.

Asked by the New York Times how his proposed ban on Muslims would apply to Mr Khan, Mr Trump said: "There will always be exceptions."

But the offer was brusquely brushed aside by Mr Khan who warned that the billionaire businessman's outspoken views on Islam risked endangering people on both sides of the Atlantic.

"Donald Trump's ignorant view of Islam could make both of our countries less safe - it risks alienating mainstream Muslims around the world and plays into the hands of extremists," he said.

"This isn't just about me - it's about my friends, my family and everyone who comes from a background similar to mine, anywhere in the world," he said.

"Donald Trump and those around him think that Western liberal values are incompatible with mainstream Islam - London has proved him wrong."

Earlier Mr Khan had warned that if he wanted to meet his counterparts in New York and Chicago, he would have to go before the presidential inauguration in January in case Mr Trump succeeded in gaining the White House.

"I want to go to America to meet with and engage with American mayors.

"If Donald Trump becomes the president I'll be stopped from going there by virtue of my faith, which means I can't engage with American mayors and swap ideas," he told Time magazine.

However Mr Trump, who has been seeking to soften his image since all but clinching the Republican nomination, insisted that he welcomed Mr Khan's election.

"I was happy to see that. I think it's a very good thing, and I hope he does a very good job because, frankly, that would be very, very good," he said.

"Because I think if he does a great job, it will really - you lead by example, always lead by example. If he does a good job, and frankly if he does a great job, that would be a terrific thing."

During the mayoral election Mr Khan repeatedly attacked his Conservative rival Zac Goldsmith for adopting Trump-like tactics, accusing him of running a campaign based on fear and division.

A Downing Street spokesman said that David Cameron had "made it very clear he doesn't agree with Donald Trump's comments about banning Muslims from the US".

Mr Cameron previously described Mr Trump's suggestion of a "shutdown" on Muslims entering the US as "divisive, stupid and wrong".

The Number 10 spokesman said: "The PM is proud of representing a country which is one of the most successful multi-racial, multi-faith, multi-ethnic countries anywhere in the world."

The mayor of Paris Anne Hidalgo said Mr Trump is "very stupid" while on a visit to London to meet Mr Khan.

She was scathing about the Republican presidential hopeful's policy of banning all Muslims from the US - but making an exception for Mr Khan.

She said: "Donald Trump is stupid, he is very stupid."

She said people of all religions, including Catholics and Muslims, do not agree with Mr Trump, adding: "Mr Trump is so stupid, my God, my God."

Asked if he would visit the US if Mr Trump did manage to enforce the policy, Mr Khan dodged the question.

Speaking to French and British reporters on a cramped platform at St Pancras International, where he warmly greeted the Paris mayor, he said: "Can I say it's an honour to have Anne here in London.

"What's really important is the similarities Paris and London have - they are the most diverse cities in the world.

"This is an example of the best of our cities - men, women, Muslims, Christians, mayors working together to work for our cities.

"Solving the housing crisis, fixing the air quality, addressing the challenges of integration and making sure our cities are safe.

"Our message to Donald Trump is this is how you work together. This is the best of humanity, this is the best of the West."

He added: "You can be a Parisian mayor and a London mayor and work closely together.

"I hope Donald Trump looks at the lessons that London sent last Thursday and recognises that it's possible to be Western and Muslim and to be friends with a mayor of Paris as well."

The two politicians stressed that they have more than just politics in common - both their mothers were dressmakers.

Speaking about how he hopes to work with his Parisian counterpart, Mr Khan said he "saw with horror" the terrorist attacks on the French capital.

He said the two mayors will work together to improve the security of the two cities.

The two toasted their relationship with a glass of water as they had a meeting in a cafe at St Pancras station.